In general, DLMCOL is very competitive for very difficult instances of medium size such as DSJC500.5 and flat300_28_0. Notably DLMCOL can find a legal solution for the instance DSJC500.5 with \(k=47\)  colors with a success rate of 5/10 (only two reference algorithms QA-COL [1]} and HEAD [2]} can reach this result occasionally with a specific fine tuning of the hyperparameters for this given instance and a low success rate of 2/10 and 2/10000 respectively). DLMCOL can also find a solution with \(k=28\)  for the instance flat300_28_0 which is difficult for the two best competitors QA-COL [3]}, [4]}, [1]} and HEAD [2]}.
For this instance flat300_28_0, performing a huge exploration of the search space with an important population is very beneficial, as it seems that there exists only one legal solution with \(k=28\)  colors. Indeed, dozens of solutions found by our algorithm were always the same up to color permutation.
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